Problem: Solve for $x$ and $y$ using elimination. ${5x+5y = 55}$ ${-2x+6y = 50}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $2$ and the bottom equation by $5$ ${10x+10y = 110}$ $-10x+30y = 250$ Add the top and bottom equations together. $40y = 360$ $\dfrac{40y}{{40}} = \dfrac{360}{{40}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {5x+5y = 55}\thinspace$ to find $x$ ${5x + 5}{(9)}{= 55}$ $5x+45 = 55$ $5x+45{-45} = 55{-45}$ $5x = 10$ $\dfrac{5x}{{5}} = \dfrac{10}{{5}}$ ${x = 2}$ You can also plug ${y = 9}$ into $\thinspace {-2x+6y = 50}\thinspace$ and get the same answer for $x$ : ${-2x + 6}{(9)}{= 50}$ ${x = 2}$